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Circuit Terminology

Circuit Terminology

An electrical network is a system composed of interconnected elements, such as resistors, capacitors, inductors, and voltage or current sources. Unlike a circuit, an electrical network does not necessarily form a closed path. In other words, while all circuits can be considered networks due to their interconnected nature, not every network qualifies as a circuit.
A circuit, on the other hand, is also an interconnected system of electrical elements but must contain one or more closed paths.

Equivalent Resistance

Equivalent Resistance

In circuit analysis, situations often arise where resistors are neither in series nor parallel configurations. To tackle such scenarios, three-terminal equivalent networks like the wye (Y) (Figure 1 (a)) or tee (T) and delta (Δ) (Figure 1 (b)) or pi (π) networks come into play. These networks offer versatile solutions and are frequently encountered in various applications, including three-phase electrical systems, electrical filters, and matching networks.

Network Function of a Circuit

Network Function of a Circuit

Frequency response analysis in electrical circuits provides vital insights into a circuit's behavior as the frequency of the input signal changes. The transfer function, a mathematical tool, is instrumental in understanding this behavior. It defines the relationship between phasor output and input and comes in four types: voltage gain, current gain, transfer impedance, and transfer admittance. The critical components of the transfer function are the poles and zeros.

Resistance and Conductance

Resistance and Conductance

A conductor's DC resistance at a given temperature is influenced by its resistivity, length, and cross-sectional area. Resistivity is an inherent property of the conductor material, with annealed copper serving as the international standard for measurement. For instance, the resistivity of hard-drawn aluminum at 20 degrees Celsius is 61% of the standard conductivity of annealed copper.
Various factors impact the resistance of a conductor. Spiraling in stranded conductors increases their...

Protein Networks

Protein Networks

An organism can have thousands of different proteins, and these proteins must cooperate to ensure the health of an organism. Proteins bind to other proteins and form complexes to carry out their functions. Many proteins interact with multiple other proteins creating a complex network of protein interactions.
These interactions can be represented through maps depicting protein-protein interaction networks, represented as nodes and edges. Nodes are circles that are representative of a protein,...

Protein Networks

Protein Networks

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Modeling Biological Membranes with Circuit Boards and Measuring Electrical Signals in Axons: Student Laboratory Exercises

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Phylogenetic Networks as Circuits With Resistance Distance.

Stefan Forcey¹, Drew Scalzo¹

¹Department of Mathematics, The University of Akron, Akron, OH, United States.

Frontiers in Genetics

|November 16, 2020

Summary

Reconstructing phylogenetic networks is challenging. This study introduces resistance distance, analogous to electrical resistance, enabling precise network reconstruction and revealing mathematical properties for accurate phylogenetic network analysis.

Keywords:

circuit linear program (LP)phylogenetic network polytope resistance

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Area of Science:

Computational Biology
Phylogenetics
Graph Theory

Background:

Phylogenetic network reconstruction is a complex problem in computational biology.
Traditional methods face challenges in accurately representing evolutionary relationships, especially with reticulate evolution.

Purpose of the Study:

To propose and investigate the utility of resistance distance as a novel approach for phylogenetic network reconstruction.
To demonstrate the mathematical properties of resistance distance and its application to network analysis.

Main Methods:

Analogizing genetic distance in phylogenetic networks to electrical resistance in graph theory.
Applying resistance distance to weighted 1-nested phylogenetic networks.
Utilizing graph theory and linear programming for network reconstruction.

Main Results:

Resistance distance for weighted 1-nested networks is identified as Kalmanson.
The unique associated circular split network fully represents the splits of the original phylogenetic network.
Reconstruction of the unweighted class of the original network is achievable via Neighbor-Net or linear programming.

Conclusions:

Resistance distance offers a powerful mathematical framework for precise phylogenetic network reconstruction.
This approach provides a new perspective on understanding evolutionary relationships and network structures.
Initial investigations into 2-nested networks using resistance distance show promising results.